The consensus of this thread seems to be to kind of suggest that villains are (or should be) people too, within the context of the story and that they should therefore have a strong, justified motivation. I don't think that's strictly true. Be prepared for graphic scenes of references to literature, anime, tv shows, and films.
All stories are driven on conflict between the protagonist and the antagonist. Because the antagonist is what stops the protagonist achieving their goals, they are frequently typically 'villainous', in order to, uh, vilify them and make it easier for the audience to identify with the protagonist. For example, in WW2 films, it's abundantly clear that the Holocaust-mongers are the bad guys because they're behaving like assholes - we therefore root for the protagonists. If you have a strong villain, even if they're hammy or clichéd, you will probably have a strong narrative.
Who says anything about a villain having to have a good motive, though? In Othello, Shakespeare gives Iago all of one line to justify his woolly motive (iirc; he was passed up for promotion in favour of Othello), which is given as part of a soliloquy and thus only and explicitly for the audience's benefit. It doesn't make his scheming against Othello throughout the rest of the play any less villainous, however. Everything Iago does and is is in service of his slightly rubbish desire to cause Othello's downfall - and explicitly says or does nothing else once Othello's ordeal is over because he's done his bit. Does it make him any less deep as a villain? Perhaps. Does the play suffer for it on the whole? Not remotely. The play is not about Iago. The play is about Othello's downfall; it's Othello we care about - which is something I think can easily trip RPers up.
Since RPing is telling one story from many PoV's (as I see it), one would think it lends itself to including villainous characters, but I'm not so certain that strong villains or antagonists are actual major agents in fiction - there are certainly many examples of strong villains and antagonists barely taking action, whether literally or more generally. While Iago doesn't shut up in Othello, he actually
does little beyond talking the other characters into torturing themselves with their own personalities. Jaws is widely considered to have been so scary because of the suspense of the shark not really appearing in shot very much. In Harry Potter, if Voldemort's going to turn up, he's going to wait until the end of the book. In Doctor Who's reboot, the villainous force of the finale of a given season appears briefly or is hinted at throughout the season (and is assumed to be responsible for at least some of the disasters of the week) before appearing in the final two episodes of the run. Much of whatever actions any of these characters do take is off-screen - and therefore, a PC that is also the (known) villain who is posting at the same regularity as the other PC's is not in keeping with the trend here.
Of course, as Elri says, the villain need not be known to the audience or the other characters, and therefore taking action on-screen remains in keeping with that trend, because it is typically ambiguous and amid red herrings anyway - Agatha Christie's bread and butter.
I think this trend exists because the antagonist has a narrative advantage - in order for there to be a plot, they must be a sufficient threat to overcome, otherwise the audience doesn't care. We don't actually need to see the antagonist or villain
do very much in order to believe that they are a threat, and they certainly don't have to appear in person to hinder the protagonist. Giovanni is the highly unsympathetic villain and overarching antagonist in the original cartoon series of Pokemon, but it's the comically incompetent Jessie and James that get sent to bother the protagonists. While they are also antagonists and villains, they couldn't really be said to be particularly threatening. However, by using them as Giovanni's proxies, it implies his authority (and therefore, asskicking quotient) and
preserves it, because the audience doesn't actually know very much about him as an individual or purely as a combative opponent.
A common thread in these examples, by the way, is a surprisingly simple motive, when reduced to its essence.
Iago missed a job opportunity. Revenge.
Team Rocket want Pokemon to make money (somehow?). Money and (implicitly) power.
Voldemort hates muggles because he's incapable of love and has a sad childhood where muggles are concerned. Psychosis + revenge.
The Joker just wants "to watch the world burn". Blue and Orange Morality.
Any culprit from Agatha Christie. All of the above (apart from eating people).
All fiction is derivative. No plot has not done before, in essence. Your villain will have the same general motive as another villain from somewhere else down the line. Napoleon the pig from Animal Farm is in it for material wealth and agency; just like Team Rocket. But they're not the same villains, and Animal Farm is no less disturbing to me because I can find similar motivations between anime villains fifty years Animal Farm's junior. It seems to me to be about style, rather than substance - not necessarily a criticism.
It's about finding the right balance for your world and your plot, and working out how those actions that the villain takes gives the work the right tone. Jessie and James maintain a comical, child-friendly tone by squabbling, being stupid, and generally fucking things up; when Giovanni steps in, it's gonna be a lot more serious because he packs a lot more heat than his cronies. Note that this works even with the predictably simple motive of Money&Power. The Dark Knight is a lot darker with themes of legitimate Chaos, and it sets that tone by raising the actual damage output of its villain: the Joker blows shit up, and people die. Extremely srs business indeed.
Long story short:Less is more.
Clichés are fine.
Style over substance.